LMFDB - Embedded newform 152.6.b.b.75.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,6,Mod(75,152)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("152.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	152.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.3783406116$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.17
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.18

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.93566 - 2.76392i) q^{2} +28.5036i q^{3} +(16.7215 + 27.2836i) q^{4} -107.944i q^{5} +(78.7817 - 140.684i) q^{6} -87.6251i q^{7} +(-7.12184 - 180.879i) q^{8} -569.454 q^{9} +O(q^{10})$	\(q+(-4.93566 - 2.76392i) q^{2} +28.5036i q^{3} +(16.7215 + 27.2836i) q^{4} -107.944i q^{5} +(78.7817 - 140.684i) q^{6} -87.6251i q^{7} +(-7.12184 - 180.879i) q^{8} -569.454 q^{9} +(-298.348 + 532.773i) q^{10} +486.899 q^{11} +(-777.679 + 476.622i) q^{12} -416.772 q^{13} +(-242.189 + 432.488i) q^{14} +3076.78 q^{15} +(-464.785 + 912.442i) q^{16} +384.824 q^{17} +(2810.63 + 1573.93i) q^{18} +(-888.357 + 1298.81i) q^{19} +(2945.08 - 1804.97i) q^{20} +2497.63 q^{21} +(-2403.17 - 1345.75i) q^{22} +4435.79i q^{23} +(5155.70 - 202.998i) q^{24} -8526.81 q^{25} +(2057.05 + 1151.93i) q^{26} -9305.09i q^{27} +(2390.72 - 1465.22i) q^{28} -4617.64 q^{29} +(-15185.9 - 8503.97i) q^{30} -1290.41 q^{31} +(4815.94 - 3218.87i) q^{32} +13878.4i q^{33} +(-1899.36 - 1063.62i) q^{34} -9458.56 q^{35} +(-9522.10 - 15536.7i) q^{36} +4994.11 q^{37} +(7974.45 - 3955.16i) q^{38} -11879.5i q^{39} +(-19524.7 + 768.757i) q^{40} +7495.86i q^{41} +(-12327.4 - 6903.25i) q^{42} -3332.16 q^{43} +(8141.67 + 13284.3i) q^{44} +61468.8i q^{45} +(12260.2 - 21893.6i) q^{46} -4616.83i q^{47} +(-26007.9 - 13248.0i) q^{48} +9128.84 q^{49} +(42085.4 + 23567.4i) q^{50} +10968.8i q^{51} +(-6969.05 - 11371.0i) q^{52} -21437.8 q^{53} +(-25718.5 + 45926.8i) q^{54} -52557.6i q^{55} +(-15849.6 + 624.052i) q^{56} +(-37020.9 - 25321.4i) q^{57} +(22791.1 + 12762.8i) q^{58} +28840.3i q^{59} +(51448.2 + 83945.4i) q^{60} +10468.1i q^{61} +(6369.03 + 3566.59i) q^{62} +49898.4i q^{63} +(-32666.6 + 2576.39i) q^{64} +44987.9i q^{65} +(38358.7 - 68498.9i) q^{66} +31728.8i q^{67} +(6434.82 + 10499.4i) q^{68} -126436. q^{69} +(46684.2 + 26142.7i) q^{70} -8413.83 q^{71} +(4055.56 + 103002. i) q^{72} +15979.4 q^{73} +(-24649.2 - 13803.3i) q^{74} -243044. i q^{75} +(-50290.9 - 2519.46i) q^{76} -42664.6i q^{77} +(-32834.0 + 58633.2i) q^{78} -33428.3 q^{79} +(98492.2 + 50170.5i) q^{80} +126851. q^{81} +(20718.0 - 36997.0i) q^{82} -59792.9 q^{83} +(41764.0 + 68144.2i) q^{84} -41539.2i q^{85} +(16446.4 + 9209.83i) q^{86} -131619. i q^{87} +(-3467.62 - 88069.9i) q^{88} -95051.2i q^{89} +(169895. - 303389. i) q^{90} +36519.7i q^{91} +(-121024. + 74173.0i) q^{92} -36781.3i q^{93} +(-12760.6 + 22787.1i) q^{94} +(140199. + 95892.4i) q^{95} +(91749.4 + 137271. i) q^{96} +48320.2i q^{97} +(-45056.9 - 25231.4i) q^{98} -277266. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.93566	−	2.76392i	−0.872510	−	0.488597i
$2$	−4.93566	−	2.76392i	−0.872510	−	0.488597i
$3$			28.5036i			1.82850i	0.405145	+	0.914252i	$0.367221\pi$
$3$			28.5036i			1.82850i	−0.405145	+	0.914252i	$0.632779\pi$
$4$	16.7215	+	27.2836i	0.522546	+	0.852611i
$5$		−	107.944i		−	1.93095i	−0.260491	−	0.965476i	$-0.583884\pi$
$5$		−	107.944i		−	1.93095i	0.260491	−	0.965476i	$-0.416116\pi$
$6$	78.7817	−	140.684i	0.893402	−	1.59539i
$7$		−	87.6251i		−	0.675902i	−0.941164	−	0.337951i	$-0.890266\pi$
$7$		−	87.6251i		−	0.675902i	0.941164	−	0.337951i	$-0.109734\pi$
$8$	−7.12184	−	180.879i	−0.0393430	−	0.999226i
$9$	−569.454			−2.34343
$10$	−298.348	+	532.773i	−0.943458	+	1.68477i
$11$	486.899			1.21327			0.606635	−	0.794981i	$-0.292519\pi$
$11$	486.899			1.21327			0.606635	+	0.794981i	$0.292519\pi$
$12$	−777.679	+	476.622i	−1.55900	+	0.955478i
$13$	−416.772			−0.683976			−0.341988	−	0.939704i	$-0.611100\pi$
$13$	−416.772			−0.683976			−0.341988	+	0.939704i	$0.611100\pi$
$14$	−242.189	+	432.488i	−0.330243	+	0.589731i
$15$	3076.78			3.53076
$16$	−464.785	+	912.442i	−0.453892	+	0.891057i
$17$	384.824			0.322953			0.161477	−	0.986877i	$-0.448374\pi$
$17$	384.824			0.322953			0.161477	+	0.986877i	$0.448374\pi$
$18$	2810.63	+	1573.93i	2.04467	+	1.14499i
$19$	−888.357	+	1298.81i	−0.564552	+	0.825398i
$19$	−888.357	+	1298.81i	−0.564552	+	0.825398i
$20$	2945.08	−	1804.97i	1.64635	−	1.00901i
$21$	2497.63			1.23589
$22$	−2403.17	−	1345.75i	−1.05859	−	0.592800i
$23$			4435.79i			1.74844i	0.485526	+	0.874222i	$0.338628\pi$
$23$			4435.79i			1.74844i	−0.485526	+	0.874222i	$0.661372\pi$
$24$	5155.70	−	202.998i	1.82709	−	0.0719389i
$25$	−8526.81			−2.72858
$26$	2057.05	+	1151.93i	0.596775	+	0.334188i
$27$		−	9305.09i		−	2.45647i
$28$	2390.72	−	1465.22i	0.576281	−	0.353190i
$29$	−4617.64			−1.01959			−0.509794	−	0.860296i	$-0.670279\pi$
$29$	−4617.64			−1.01959			−0.509794	+	0.860296i	$0.670279\pi$
$30$	−15185.9	−	8503.97i	−3.08062	−	1.72512i
$31$	−1290.41			−0.241170			−0.120585	−	0.992703i	$-0.538477\pi$
$31$	−1290.41			−0.241170			−0.120585	+	0.992703i	$0.538477\pi$
$32$	4815.94	−	3218.87i	0.831393	−	0.555686i
$33$			13878.4i			2.21847i
$34$	−1899.36	−	1063.62i	−0.281780	−	0.157794i
$35$	−9458.56			−1.30513
$36$	−9522.10	−	15536.7i	−1.22455	−	1.99803i
$37$	4994.11			0.599728			0.299864	−	0.953982i	$-0.403059\pi$
$37$	4994.11			0.599728			0.299864	+	0.953982i	$0.403059\pi$
$38$	7974.45	−	3955.16i	0.895864	−	0.444329i
$39$		−	11879.5i		−	1.25065i
$40$	−19524.7	+	768.757i	−1.92946	+	0.0759695i
$41$			7495.86i			0.696405i	0.937419	+	0.348203i	$0.113208\pi$
$41$			7495.86i			0.696405i	−0.937419	+	0.348203i	$0.886792\pi$
$42$	−12327.4	−	6903.25i	−1.07833	−	0.603852i
$43$	−3332.16			−0.274824			−0.137412	−	0.990514i	$-0.543878\pi$
$43$	−3332.16			−0.274824			−0.137412	+	0.990514i	$0.543878\pi$
$44$	8141.67	+	13284.3i	0.633989	+	1.03445i
$45$			61468.8i			4.52505i
$46$	12260.2	−	21893.6i	0.854285	−	1.52553i
$47$		−	4616.83i		−	0.304859i	−0.988314	−	0.152429i	$-0.951290\pi$
$47$		−	4616.83i		−	0.304859i	0.988314	−	0.152429i	$-0.0487097\pi$
$48$	−26007.9	−	13248.0i	−1.62930	−	0.829943i
$49$	9128.84			0.543157
$50$	42085.4	+	23567.4i	2.38071	+	1.33318i
$51$			10968.8i			0.590521i
$52$	−6969.05	−	11371.0i	−0.357409	−	0.583165i
$53$	−21437.8			−1.04831			−0.524155	−	0.851623i	$-0.675619\pi$
$53$	−21437.8			−1.04831			−0.524155	+	0.851623i	$0.675619\pi$
$54$	−25718.5	+	45926.8i	−1.20022	+	2.14329i
$55$		−	52557.6i		−	2.34277i
$56$	−15849.6	+	624.052i	−0.675378	+	0.0265920i
$57$	−37020.9	−	25321.4i	−1.50924	−	1.03229i
$58$	22791.1	+	12762.8i	0.889601	+	0.498168i
$59$			28840.3i			1.07862i	0.842106	+	0.539312i	$0.181316\pi$
$59$			28840.3i			1.07862i	−0.842106	+	0.539312i	$0.818684\pi$
$60$	51448.2	+	83945.4i	1.84498	+	3.01036i
$61$			10468.1i			0.360199i	0.983648	+	0.180099i	$0.0576419\pi$
$61$			10468.1i			0.360199i	−0.983648	+	0.180099i	$0.942358\pi$
$62$	6369.03	+	3566.59i	0.210423	+	0.117835i
$63$			49898.4i			1.58393i
$64$	−32666.6	+	2576.39i	−0.996904	+	0.0786251i
$65$			44987.9i			1.32072i
$66$	38358.7	−	68498.9i	1.08394	−	1.93564i
$67$			31728.8i			0.863509i	0.901991	+	0.431755i	$0.142105\pi$
$67$			31728.8i			0.863509i	−0.901991	+	0.431755i	$0.857895\pi$
$68$	6434.82	+	10499.4i	0.168758	+	0.275353i
$69$	−126436.			−3.19704
$70$	46684.2	+	26142.7i	1.13874	+	0.637685i
$71$	−8413.83			−0.198083			−0.0990417	−	0.995083i	$-0.531578\pi$
$71$	−8413.83			−0.198083			−0.0990417	+	0.995083i	$0.531578\pi$
$72$	4055.56	+	103002.i	0.0921976	+	2.34162i
$73$	15979.4			0.350956			0.175478	−	0.984483i	$-0.443853\pi$
$73$	15979.4			0.350956			0.175478	+	0.984483i	$0.443853\pi$
$74$	−24649.2	−	13803.3i	−0.523268	−	0.293025i
$75$		−	243044.i		−	4.98922i
$76$	−50290.9	−	2519.46i	−0.998747	−	0.0500349i
$77$		−	42664.6i		−	0.820051i
$78$	−32834.0	+	58633.2i	−0.611065	+	1.09121i
$79$	−33428.3			−0.602625			−0.301313	−	0.953525i	$-0.597425\pi$
$79$	−33428.3			−0.602625			−0.301313	+	0.953525i	$0.597425\pi$
$80$	98492.2	+	50170.5i	1.72059	+	0.876443i
$81$	126851.			2.14824
$82$	20718.0	−	36997.0i	0.340262	−	0.607620i
$83$	−59792.9			−0.952695			−0.476348	−	0.879257i	$-0.658040\pi$
$83$	−59792.9			−0.952695			−0.476348	+	0.879257i	$0.658040\pi$
$84$	41764.0	+	68144.2i	0.645809	+	1.05373i
$85$		−	41539.2i		−	0.623607i
$86$	16446.4	+	9209.83i	0.239787	+	0.134278i
$87$		−	131619.i		−	1.86432i
$88$	−3467.62	−	88069.9i	−0.0477337	−	1.21233i
$89$		−	95051.2i		−	1.27199i	−0.771695	−	0.635993i	$-0.780591\pi$
$89$		−	95051.2i		−	1.27199i	0.771695	−	0.635993i	$-0.219409\pi$
$90$	169895.	−	303389.i	2.21093	−	3.94815i
$91$			36519.7i			0.462300i
$92$	−121024.	+	74173.0i	−1.49074	+	0.913642i
$93$		−	36781.3i		−	0.440981i
$94$	−12760.6	+	22787.1i	−0.148953	+	0.265992i
$95$	140199.	+	95892.4i	1.59380	+	1.09012i
$96$	91749.4	+	137271.i	1.01607	+	1.52021i
$97$			48320.2i			0.521434i	0.965415	+	0.260717i	$0.0839590\pi$
$97$			48320.2i			0.521434i	−0.965415	+	0.260717i	$0.916041\pi$
$98$	−45056.9	−	25231.4i	−0.473910	−	0.265385i
$99$	−277266.			−2.84321
$100$	−142581.	−	232642.i	−1.42581	−	2.32642i
$101$			107308.i			1.04671i	0.852114	+	0.523356i	$0.175320\pi$
$101$			107308.i			1.04671i	−0.852114	+	0.523356i	$0.824680\pi$
$102$	30317.0	−	54138.5i	0.288527	−	0.515235i
$103$	−104875.			−0.974044			−0.487022	−	0.873390i	$-0.661917\pi$
$103$	−104875.			−0.974044			−0.487022	+	0.873390i	$0.661917\pi$
$104$	2968.19	+	75385.5i	0.0269097	+	0.683446i
$105$		−	269603.i		−	2.38644i
$106$	105809.	+	59252.3i	0.914660	+	0.512201i
$107$			199273.i			1.68264i	0.540541	+	0.841318i	$0.318220\pi$
$107$			199273.i			1.68264i	−0.540541	+	0.841318i	$0.681780\pi$
$108$	253876.	−	155595.i	2.09441	−	1.28362i
$109$	−126980.			−1.02369			−0.511846	−	0.859077i	$-0.671038\pi$
$109$	−126980.			−1.02369			−0.511846	+	0.859077i	$0.671038\pi$
$110$	−145265.	+	259406.i	−1.14467	+	2.04409i
$111$			142350.i			1.09661i
$112$	79952.8	+	40726.8i	0.602267	+	0.306786i
$113$		−	114899.i		−	0.846486i	−0.906016	−	0.423243i	$-0.860892\pi$
$113$		−	114899.i		−	0.846486i	0.906016	−	0.423243i	$-0.139108\pi$
$114$	112736.	+	227300.i	0.812458	+	1.63809i
$115$	478815.			3.37616
$116$	−77213.7	−	125986.i	−0.532782	−	0.869313i
$117$	237333.			1.60285
$118$	79712.4	−	142346.i	0.527013	−	0.941110i
$119$		−	33720.2i		−	0.218284i
$120$	−21912.3	−	556525.i	−0.138911	−	3.52802i
$121$	76019.7			0.472022
$122$	28932.9	−	51666.8i	0.175992	−	0.314277i
$123$	−213659.			−1.27338
$124$	−21577.6	−	35207.0i	−0.126022	−	0.205624i
$125$			583090.i			3.33780i
$126$	137915.	−	246282.i	0.773903	−	1.38199i
$127$	80625.9			0.443573			0.221787	−	0.975095i	$-0.428811\pi$
$127$	80625.9			0.443573			0.221787	+	0.975095i	$0.428811\pi$
$128$	168352.	+	77571.7i	0.908224	+	0.418483i
$129$		−	94978.4i		−	0.502517i
$130$	124343.	−	222045.i	0.645302	−	1.15234i
$131$	23779.3			0.121066			0.0605329	−	0.998166i	$-0.480720\pi$
$131$	23779.3			0.121066			0.0605329	+	0.998166i	$0.480720\pi$
$132$	−378651.	+	232067.i	−1.89149	+	1.15925i
$133$	113809.	+	77842.4i	0.557888	+	0.381581i
$134$	87696.0	−	156603.i	0.421908	−	0.753420i
$135$	−1.00442e6			−4.74333
$136$	−2740.65	−	69606.6i	−0.0127059	−	0.322703i
$137$	44390.8			0.202065			0.101033	−	0.994883i	$-0.467785\pi$
$137$	44390.8			0.202065			0.101033	+	0.994883i	$0.467785\pi$
$138$	624045.	+	349459.i	2.78945	+	1.56206i
$139$	−265338.			−1.16483			−0.582415	−	0.812892i	$-0.697892\pi$
$139$	−265338.			−1.16483			−0.582415	+	0.812892i	$0.697892\pi$
$140$	−158161.	−	258063.i	−0.681992	−	1.11277i
$141$	131596.			0.557436
$142$	41527.8	+	23255.2i	0.172830	+	0.0967829i
$143$	−202926.			−0.829847
$144$	264673.	−	519593.i	1.06366	−	2.08813i
$145$			498444.i			1.96878i
$146$	−78868.8	−	44165.8i	−0.306213	−	0.171476i
$147$			260205.i			0.993165i
$148$	83508.9	+	136257.i	0.313385	+	0.511335i
$149$		−	189532.i		−	0.699385i	−0.936864	−	0.349693i	$-0.886286\pi$
$149$		−	189532.i		−	0.699385i	0.936864	−	0.349693i	$-0.113714\pi$
$150$	−671756.	+	1.19958e6i	−2.43772	+	4.35314i
$151$	231618.			0.826666			0.413333	−	0.910580i	$-0.364364\pi$
$151$	231618.			0.826666			0.413333	+	0.910580i	$0.364364\pi$
$152$	241255.	+	151435.i	0.846970	+	0.531641i
$153$	−219139.			−0.756818
$154$	−117922.	+	210578.i	−0.400674	+	0.715502i
$155$			139291.i			0.465688i
$156$	324115.	−	198643.i	1.06632	−	0.653523i
$157$			14527.3i			0.0470365i	0.999723	+	0.0235182i	$0.00748678\pi$
$157$			14527.3i			0.0470365i	−0.999723	+	0.0235182i	$0.992513\pi$
$158$	164991.	+	92393.3i	0.525796	+	0.294441i
$159$		−	611052.i		−	1.91684i
$160$	−347457.	−	519850.i	−1.07300	−	1.60538i
$161$	388687.			1.18178
$162$	−626094.	−	350607.i	−1.87436	−	1.04962i
$163$	365221.			1.07668			0.538340	−	0.842728i	$-0.319052\pi$
$163$	365221.			1.07668			0.538340	+	0.842728i	$0.319052\pi$
$164$	−204514.	+	125342.i	−0.593763	+	0.363904i
$165$	1.49808e6			4.28376
$166$	295117.	+	165263.i	0.831236	+	0.465484i
$167$	64713.3			0.179557			0.0897785	−	0.995962i	$-0.471384\pi$
$167$	64713.3			0.179557			0.0897785	+	0.995962i	$0.471384\pi$
$168$	−17787.7	−	451769.i	−0.0486236	−	1.23493i
$169$	−197594.			−0.532177
$170$	−114811.	+	205023.i	−0.304693	+	0.544103i
$171$	505878.	−	739615.i	1.32299	−	1.93426i
$172$	−55718.6	−	90913.2i	−0.143608	−	0.234318i
$173$	240415.			0.610725			0.305362	−	0.952236i	$-0.401222\pi$
$173$	240415.			0.610725			0.305362	+	0.952236i	$0.401222\pi$
$174$	−363785.	+	649628.i	−0.910903	+	1.62664i
$175$			747162.i			1.84425i
$176$	−226303.	+	444267.i	−0.550693	+	1.08109i
$177$	−822052.			−1.97227
$178$	−262714.	+	469140.i	−0.621489	+	1.10982i
$179$			274685.i			0.640770i	0.947287	+	0.320385i	$0.103812\pi$
$179$			274685.i			0.640770i	−0.947287	+	0.320385i	$0.896188\pi$
$180$	−1.67709e6	+	1.02785e6i	−3.85811	+	2.36455i
$181$	−553197.			−1.25512			−0.627558	−	0.778570i	$-0.715945\pi$
$181$	−553197.			−1.25512			−0.627558	+	0.778570i	$0.715945\pi$
$182$	100938.	−	180249.i	0.225879	−	0.403361i
$183$	−298377.			−0.658625
$184$	802343.	−	31591.0i	1.74709	−	0.0687890i
$185$		−	539082.i		−	1.15805i
$186$	−101661.	+	181540.i	−0.215462	+	0.384760i
$187$	187370.			0.391829
$188$	125963.	−	77200.1i	0.259926	−	0.159303i
$189$	−815360.			−1.66033
$190$	−426934.	−	860791.i	−0.857979	−	1.72987i
$191$		−	566777.i		−	1.12416i	−0.827082	−	0.562081i	$-0.810001\pi$
$191$		−	566777.i		−	1.12416i	0.827082	−	0.562081i	$-0.189999\pi$
$192$	−73436.2	−	931114.i	−0.143766	−	1.82284i
$193$		−	682223.i		−	1.31836i	−0.751986	−	0.659179i	$-0.770904\pi$
$193$		−	682223.i		−	1.31836i	0.751986	−	0.659179i	$-0.229096\pi$
$194$	133553.	−	238492.i	0.254771	−	0.454956i
$195$	−1.28232e6			−2.41495
$196$	152648.	+	249067.i	0.283825	+	0.463102i
$197$		−	202201.i		−	0.371208i	−0.982625	−	0.185604i	$-0.940576\pi$
$197$		−	202201.i		−	0.371208i	0.982625	−	0.185604i	$-0.0594242\pi$
$198$	1.36849e6	+	766343.i	2.48073	+	1.38918i
$199$			56553.1i			0.101233i	0.998718	+	0.0506167i	$0.0161187\pi$
$199$			56553.1i			0.101233i	−0.998718	+	0.0506167i	$0.983881\pi$
$200$	60726.6	+	1.54232e6i	0.107350	+	2.72647i
$201$	−904385.			−1.57893
$202$	296590.	−	529634.i	0.511420	−	0.913266i
$203$			404621.i			0.689142i
$204$	−299269.	+	183415.i	−0.503485	+	0.308574i
$205$	809130.			1.34473
$206$	517627.	+	289866.i	0.849863	+	0.475915i
$207$		−	2.52598e6i		−	4.09736i
$208$	193710.	−	380281.i	0.310451	−	0.609461i
$209$	−432540.	+	632392.i	−0.684953	+	1.00143i
$210$	−745161.	+	1.33067e6i	−1.16601	+	2.08220i
$211$			218513.i			0.337887i	0.985626	+	0.168943i	$0.0540355\pi$
$211$			218513.i			0.337887i	−0.985626	+	0.168943i	$0.945965\pi$
$212$	−358471.	−	584898.i	−0.547790	−	0.893800i
$213$		−	239824.i		−	0.362196i
$214$	550776.	−	983546.i	0.822131	−	1.46812i
$215$			359685.i			0.530672i
$216$	−1.68310e6	+	66269.4i	−2.45457	+	0.0966449i
$217$			113072.i			0.163007i
$218$	626731.	+	350963.i	0.893182	+	0.500173i
$219$			455469.i			0.641725i
$220$	1.43396e6	−	878840.i	1.99747	−	1.22420i
$221$	−160384.			−0.220892
$222$	393445.	−	702592.i	0.535798	−	0.956799i
$223$	−645531.			−0.869270			−0.434635	−	0.900607i	$-0.643123\pi$
$223$	−645531.			−0.869270			−0.434635	+	0.900607i	$0.643123\pi$
$224$	−282054.	−	421997.i	−0.375589	−	0.561939i
$225$	4.85562e6			6.39423
$226$	−317572.	+	567102.i	−0.413590	+	0.738567i
$227$			484459.i			0.624012i	0.950080	+	0.312006i	$0.101001\pi$
$227$			484459.i			0.624012i	−0.950080	+	0.312006i	$0.898999\pi$
$228$	71813.5	−	1.43347e6i	0.0914891	−	1.82621i
$229$			1.03118e6i			1.29940i	0.760190	+	0.649701i	$0.225106\pi$
$229$			1.03118e6i			1.29940i	−0.760190	+	0.649701i	$0.774894\pi$
$230$	−2.36327e6	−	1.32341e6i	−2.94573	−	1.64958i
$231$	1.21609e6			1.49947
$232$	32886.1	+	835235.i	0.0401137	+	1.01880i
$233$	1.18151e6			1.42576			0.712881	−	0.701285i	$-0.247390\pi$
$233$	1.18151e6			1.42576			0.712881	+	0.701285i	$0.247390\pi$
$234$	−1.17139e6	−	655969.i	−1.39850	−	0.783147i
$235$	−498357.			−0.588668
$236$	−786867.	+	482253.i	−0.919647	+	0.563631i
$237$		−	952827.i		−	1.10190i
$238$	−93200.0	+	166431.i	−0.106653	+	0.190455i
$239$		−	146530.i		−	0.165933i	−0.996552	−	0.0829664i	$-0.973561\pi$
$239$		−	146530.i		−	0.165933i	0.996552	−	0.0829664i	$-0.0264394\pi$
$240$	−1.43004e6	+	2.80738e6i	−1.60258	+	3.14611i
$241$			1.14545e6i			1.27038i	0.772355	+	0.635191i	$0.219078\pi$
$241$			1.14545e6i			1.27038i	−0.772355	+	0.635191i	$0.780922\pi$
$242$	−375207.	−	210112.i	−0.411844	−	0.230629i
$243$			1.35457e6i			1.47159i
$244$	−285606.	+	175042.i	−0.307109	+	0.188220i
$245$		−	985399.i		−	1.04881i
$246$	1.05455e6	+	590537.i	1.11104	+	0.622170i
$247$	370243.	−	541310.i	0.386140	−	0.564552i
$248$	9190.10	+	233408.i	0.00948836	+	0.240983i
$249$		−	1.70431e6i		−	1.74201i
$250$	1.61162e6	−	2.87793e6i	1.63084	−	2.91227i
$251$	−1.93804e6			−1.94168			−0.970841	−	0.239725i	$-0.922943\pi$
$251$	−1.93804e6			−1.94168			−0.970841	+	0.239725i	$0.922943\pi$
$252$	−1.36141e6	+	834375.i	−1.35047	+	0.827675i
$253$			2.15978e6i			2.12133i
$254$	−397942.	−	222844.i	−0.387022	−	0.216729i
$255$	1.18402e6			1.14027
$256$	−616526.	−	848179.i	−0.587965	−	0.808886i
$257$			1.43835e6i			1.35841i	0.733949	+	0.679204i	$0.237675\pi$
$257$			1.43835e6i			1.35841i	−0.733949	+	0.679204i	$0.762325\pi$
$258$	−262513.	+	468781.i	−0.245528	+	0.438451i
$259$		−	437610.i		−	0.405357i
$260$	−1.22743e6	+	752264.i	−1.12606	+	0.690139i
$261$	2.62953e6			2.38934
$262$	−117367.	−	65724.3i	−0.105631	−	0.0591524i
$263$			935536.i			0.834010i	0.908904	+	0.417005i	$0.136920\pi$
$263$			935536.i			0.834010i	−0.908904	+	0.417005i	$0.863080\pi$
$264$	2.51031e6	−	98839.5i	2.21675	−	0.0872812i
$265$			2.31407e6i			2.02424i
$266$	−346571.	−	698762.i	−0.300323	−	0.605516i
$267$	2.70930e6			2.32583
$268$	−865675.	+	530553.i	−0.736238	+	0.451223i
$269$	−1.71576e6			−1.44569			−0.722845	−	0.691010i	$-0.757166\pi$
$269$	−1.71576e6			−1.44569			−0.722845	+	0.691010i	$0.757166\pi$
$270$	4.95750e6	+	2.77615e6i	4.13860	+	2.31757i
$271$		−	1.11326e6i		−	0.920817i	−0.887707	−	0.460409i	$-0.847703\pi$
$271$		−	1.11326e6i		−	0.920817i	0.887707	−	0.460409i	$-0.152297\pi$
$272$	−178860.	+	351129.i	−0.146586	+	0.287770i
$273$	−1.04094e6			−0.845318
$274$	−219098.	−	122693.i	−0.176304	−	0.0987286i
$275$	−4.15169e6			−3.31050
$276$	−2.11420e6	−	3.44962e6i	−1.67060	−	2.72583i
$277$			576274.i			0.451263i	0.974213	+	0.225631i	$0.0724445\pi$
$277$			576274.i			0.451263i	−0.974213	+	0.225631i	$0.927556\pi$
$278$	1.30962e6	+	733374.i	1.01633	+	0.569133i
$279$	734829.			0.565166
$280$	67362.4	+	1.71086e6i	0.0513479	+	1.30412i
$281$		−	1.16738e6i		−	0.881957i	−0.897518	−	0.440978i	$-0.854632\pi$
$281$		−	1.16738e6i		−	0.881957i	0.897518	−	0.440978i	$-0.145368\pi$
$282$	−649513.	−	363721.i	−0.486368	−	0.272362i
$283$	1.44951e6			1.07586			0.537931	−	0.842989i	$-0.319206\pi$
$283$	1.44951e6			1.07586			0.537931	+	0.842989i	$0.319206\pi$
$284$	−140692.	−	229559.i	−0.103508	−	0.168888i
$285$	−2.73328e6	+	3.99616e6i	−1.99329	+	2.91428i
$286$	1.00157e6	+	560872.i	0.724049	+	0.405461i
$287$	656826.			0.470701
$288$	−2.74245e6	+	1.83300e6i	−1.94831	+	1.30221i
$289$	−1.27177e6			−0.895701
$290$	1.37766e6	−	2.46015e6i	0.961939	−	1.71778i
$291$	−1.37730e6			−0.953445
$292$	267199.	+	435974.i	0.183391	+	0.299229i
$293$	448214.			0.305012			0.152506	−	0.988303i	$-0.451266\pi$
$293$	448214.			0.305012			0.152506	+	0.988303i	$0.451266\pi$
$294$	719185.	−	1.28428e6i	0.485258	−	0.866546i
$295$	3.11313e6			2.08277
$296$	−35567.3	−	903331.i	−0.0235951	−	0.599263i
$297$		−	4.53064e6i		−	2.98036i
$298$	−523851.	+	935465.i	−0.341718	+	0.610220i
$299$		−	1.84872e6i		−	1.19589i
$300$	6.63112e6	−	4.06406e6i	4.25386	−	2.60710i
$301$			291981.i			0.185754i
$302$	−1.14319e6	−	640175.i	−0.721274	−	0.403907i
$303$	−3.05865e6			−1.91392
$304$	−772198.	−	1.41424e6i	−0.479231	−	0.877689i
$305$	1.12996e6			0.695527
$306$	1.08160e6	+	605684.i	0.660331	+	0.369779i
$307$		−	2.61571e6i		−	1.58396i	−0.610550	−	0.791978i	$-0.709052\pi$
$307$		−	2.61571e6i		−	1.58396i	0.610550	−	0.791978i	$-0.290948\pi$
$308$	1.16404e6	−	713414.i	0.699184	−	0.428514i
$309$		−	2.98931e6i		−	1.78104i
$310$	384991.	−	687495.i	0.227534	−	0.406317i
$311$			2.86448e6i			1.67936i	0.543078	+	0.839682i	$0.317259\pi$
$311$			2.86448e6i			1.67936i	−0.543078	+	0.839682i	$0.682741\pi$
$312$	−2.14875e6	+	84604.0i	−1.24968	+	0.0492044i
$313$	1.94436e6			1.12180			0.560902	−	0.827882i	$-0.310455\pi$
$313$	1.94436e6			1.12180			0.560902	+	0.827882i	$0.310455\pi$
$314$	40152.2	−	71701.6i	0.0229819	−	0.0410398i
$315$	5.38621e6			3.05849
$316$	−558971.	−	912044.i	−0.314899	−	0.513805i
$317$	98182.3			0.0548763			0.0274382	−	0.999624i	$-0.491265\pi$
$317$	98182.3			0.0548763			0.0274382	+	0.999624i	$0.491265\pi$
$318$	−1.68890e6	+	3.01595e6i	−0.936562	+	1.67246i
$319$	−2.24832e6			−1.23704
$320$	278104.	+	3.52614e6i	0.151821	+	1.92498i
$321$	−5.68001e6			−3.07671
$322$	−1.91843e6	−	1.07430e6i	−1.03111	−	0.577412i
$323$	−341861.	+	499815.i	−0.182324	+	0.266565i
$324$	2.12114e6	+	3.46095e6i	1.12255	+	1.83161i
$325$	3.55374e6			1.86628
$326$	−1.80261e6	−	1.00944e6i	−0.939414	−	0.526063i
$327$		−	3.61939e6i		−	1.87183i
$328$	1.35585e6	−	53384.4i	0.695866	−	0.0273987i
$329$	−404550.			−0.206055
$330$	−7.39401e6	−	4.14057e6i	−3.73762	−	2.09303i
$331$		−	2.71655e6i		−	1.36285i	−0.731889	−	0.681424i	$-0.761361\pi$
$331$		−	2.71655e6i		−	1.36285i	0.731889	−	0.681424i	$-0.238639\pi$
$332$	−999824.	−	1.63136e6i	−0.497827	−	0.812279i
$333$	−2.84392e6			−1.40542
$334$	−319403.	−	178863.i	−0.156665	−	0.0877310i
$335$	3.42492e6			1.66740
$336$	−1.16086e6	+	2.27894e6i	−0.560960	+	1.10125i
$337$		−	1.78296e6i		−	0.855198i	−0.903968	−	0.427599i	$-0.859359\pi$
$337$		−	1.78296e6i		−	0.855198i	0.903968	−	0.427599i	$-0.140641\pi$
$338$	975255.	+	546134.i	0.464330	+	0.260020i
$339$	3.27503e6			1.54780
$340$	1.13334e6	−	694597.i	0.531694	−	0.325863i
$341$	−628300.			−0.292604
$342$	−4.54108e6	+	2.25228e6i	−2.09939	+	1.04125i
$343$		−	2.27263e6i		−	1.04302i
$344$	23731.1	+	602718.i	0.0108124	+	0.274611i
$345$			1.36479e7i			6.17333i
$346$	−1.18660e6	−	664487.i	−0.532863	−	0.298398i
$347$	−137970.			−0.0615124			−0.0307562	−	0.999527i	$-0.509792\pi$
$347$	−137970.			−0.0615124			−0.0307562	+	0.999527i	$0.509792\pi$
$348$	3.59104e6	−	2.20087e6i	1.58954	−	0.974194i
$349$		−	3.14082e6i		−	1.38032i	−0.723658	−	0.690159i	$-0.757541\pi$
$349$		−	3.14082e6i		−	1.38032i	0.723658	−	0.690159i	$-0.242459\pi$
$350$	2.06510e6	−	3.68774e6i	0.901095	−	1.60913i
$351$			3.87811e6i			1.68016i
$352$	2.34488e6	−	1.56727e6i	1.00870	−	0.674196i
$353$	2.61200e6			1.11567			0.557836	−	0.829951i	$-0.311632\pi$
$353$	2.61200e6			1.11567			0.557836	+	0.829951i	$0.311632\pi$
$354$	4.05737e6	+	2.27209e6i	1.72082	+	0.963645i
$355$			908219.i			0.382490i
$356$	2.59333e6	−	1.58939e6i	1.08451	−	0.664671i
$357$	961146.			0.399134
$358$	759207.	−	1.35575e6i	0.313078	−	0.559078i
$359$			1.36617e6i			0.559460i	0.960079	+	0.279730i	$0.0902450\pi$
$359$			1.36617e6i			0.559460i	−0.960079	+	0.279730i	$0.909755\pi$
$360$	1.11184e7	−	437771.i	4.52155	−	0.178029i
$361$	−897741.	−	2.30762e6i	−0.362563	−	0.931959i
$362$	2.73039e6	+	1.52899e6i	1.09510	+	0.613246i
$363$			2.16683e6i			0.863095i
$364$	−996388.	+	610664.i	−0.394162	+	0.241573i
$365$		−	1.72487e6i		−	0.677680i
$366$	1.47269e6	+	824692.i	0.574657	+	0.321802i
$367$		−	1.39167e6i		−	0.539349i	−0.962952	−	0.269674i	$-0.913084\pi$
$367$		−	1.39167e6i		−	0.539349i	0.962952	−	0.269674i	$-0.0869161\pi$
$368$	−4.04741e6	−	2.06169e6i	−1.55796	−	0.793604i
$369$		−	4.26855e6i		−	1.63198i
$370$	−1.48998e6	+	2.66073e6i	−0.565818	+	1.01041i
$371$			1.87849e6i			0.708554i
$372$	1.00352e6	−	615037.i	0.375985	−	0.230433i
$373$	−1.45159e6			−0.540221			−0.270110	−	0.962829i	$-0.587060\pi$
$373$	−1.45159e6			−0.540221			−0.270110	+	0.962829i	$0.587060\pi$
$374$	−924796.	−	517877.i	−0.341875	−	0.191446i
$375$	−1.66202e7			−6.10319
$376$	−835088.	+	32880.3i	−0.304623	+	0.0119941i
$377$	1.92451e6			0.697374
$378$	4.02434e6	+	2.25359e6i	1.44865	+	0.811233i
$379$		−	4.49243e6i		−	1.60651i	−0.595635	−	0.803255i	$-0.703099\pi$
$379$		−	4.49243e6i		−	1.60651i	0.595635	−	0.803255i	$-0.296901\pi$
$380$	−271959.	+	5.42858e6i	−0.0966150	+	1.92853i
$381$			2.29813e6i			0.811076i
$382$	−1.56653e6	+	2.79742e6i	−0.549262	+	0.980842i
$383$	3.85576e6			1.34311			0.671557	−	0.740953i	$-0.265626\pi$
$383$	3.85576e6			1.34311			0.671557	+	0.740953i	$0.265626\pi$
$384$	−2.21107e6	+	4.79863e6i	−0.765199	+	1.66069i
$385$	−4.60537e6			−1.58348
$386$	−1.88561e6	+	3.36722e6i	−0.644146	+	1.15028i
$387$	1.89751e6			0.644031
$388$	−1.31835e6	+	807985.i	−0.444581	+	0.272473i
$389$			5.52442e6i			1.85103i	0.378717	+	0.925513i	$0.376365\pi$
$389$			5.52442e6i			1.85103i	−0.378717	+	0.925513i	$0.623635\pi$
$390$	6.32907e6	+	3.54422e6i	2.10707	+	1.17994i
$391$			1.70700e6i			0.564665i
$392$	−65014.2	−	1.65122e6i	−0.0213694	−	0.542737i
$393$			677796.i			0.221370i
$394$	−558868.	+	997995.i	−0.181371	+	0.323883i
$395$			3.60837e6i			1.16364i
$396$	−4.63630e6	−	7.56481e6i	−1.48571	−	2.42415i
$397$			2.47956e6i			0.789584i	0.918770	+	0.394792i	$0.129183\pi$
$397$			2.47956e6i			0.789584i	−0.918770	+	0.394792i	$0.870817\pi$
$398$	156308.	−	279127.i	0.0494623	−	0.0883270i
$399$	−2.21879e6	+	3.24396e6i	−0.697723	+	1.02010i
$400$	3.96313e6	−	7.78022e6i	1.23848	−	2.43132i
$401$		−	2.59539e6i		−	0.806011i	−0.915197	−	0.403006i	$-0.867965\pi$
$401$		−	2.59539e6i		−	0.806011i	0.915197	−	0.403006i	$-0.132035\pi$
$402$	4.46374e6	+	2.49965e6i	1.37763	+	0.771461i
$403$	537808.			0.164955
$404$	−2.92773e6	+	1.79434e6i	−0.892438	+	0.546955i
$405$		−	1.36928e7i		−	4.14814i
$406$	1.11834e6	−	1.99707e6i	0.336713	−	0.601283i
$407$	2.43163e6			0.727631
$408$	1.98404e6	−	78118.4i	0.590064	−	0.0232329i
$409$		−	3.04967e6i		−	0.901457i	−0.892661	−	0.450729i	$-0.851164\pi$
$409$		−	3.04967e6i		−	0.901457i	0.892661	−	0.450729i	$-0.148836\pi$
$410$	−3.99359e6	−	2.23637e6i	−1.17329	−	0.657029i
$411$			1.26530e6i			0.369478i
$412$	−1.75366e6	−	2.86136e6i	−0.508983	−	0.830481i
$413$	2.52714e6			0.729044
$414$	−6.98161e6	+	1.24674e7i	−2.00196	+	3.57498i
$415$			6.45425e6i			1.83961i
$416$	−2.00715e6	+	1.34154e6i	−0.568652	+	0.380075i
$417$		−	7.56308e6i		−	2.12990i
$418$	3.88275e6	−	1.92576e6i	1.08692	−	0.539091i
$419$	−1.67462e6			−0.465994			−0.232997	−	0.972477i	$-0.574853\pi$
$419$	−1.67462e6			−0.465994			−0.232997	+	0.972477i	$0.574853\pi$
$420$	7.35572e6	−	4.50816e6i	2.03471	−	1.24703i
$421$	−648849.			−0.178418			−0.0892090	−	0.996013i	$-0.528434\pi$
$421$	−648849.			−0.178418			−0.0892090	+	0.996013i	$0.528434\pi$
$422$	603953.	−	1.07851e6i	0.165090	−	0.294809i
$423$			2.62907e6i			0.714416i
$424$	152676.	+	3.87764e6i	0.0412436	+	1.04750i
$425$	−3.28132e6			−0.881203
$426$	−662856.	+	1.18369e6i	−0.176968	+	0.316020i
$427$	917266.			0.243459
$428$	−5.43689e6	+	3.33215e6i	−1.43463	+	0.879254i
$429$		−	5.78412e6i		−	1.51738i
$430$	994141.	−	1.77528e6i	0.259285	−	0.463016i
$431$	−769722.			−0.199591			−0.0997955	−	0.995008i	$-0.531819\pi$
$431$	−769722.			−0.199591			−0.0997955	+	0.995008i	$0.531819\pi$
$432$	8.49036e6	+	4.32487e6i	2.18885	+	1.11497i
$433$		−	3.02139e6i		−	0.774438i	−0.921988	−	0.387219i	$-0.873436\pi$
$433$		−	3.02139e6i		−	0.774438i	0.921988	−	0.387219i	$-0.126564\pi$
$434$	312523.	−	558087.i	0.0796449	−	0.142225i
$435$	−1.42074e7			−3.59992
$436$	−2.12329e6	−	3.46447e6i	−0.534926	−	0.872812i
$437$	−5.76128e6	−	3.94057e6i	−1.44316	−	0.987087i
$438$	1.25888e6	−	2.24804e6i	0.313545	−	0.559911i
$439$	1.29727e6			0.321269			0.160634	−	0.987014i	$-0.448646\pi$
$439$	1.29727e6			0.321269			0.160634	+	0.987014i	$0.448646\pi$
$440$	−9.50658e6	+	374307.i	−2.34095	+	0.0921714i
$441$	−5.19845e6			−1.27285
$442$	791600.	+	443289.i	0.192730	+	0.107927i
$443$	1.21945e6			0.295226			0.147613	−	0.989045i	$-0.452841\pi$
$443$	1.21945e6			0.295226			0.147613	+	0.989045i	$0.452841\pi$
$444$	−3.88382e6	+	2.38030e6i	−0.934978	+	0.573027i
$445$	−1.02602e7			−2.45615
$446$	3.18612e6	+	1.78420e6i	0.758447	+	0.424723i
$447$	5.40233e6			1.27883
$448$	225756.	+	2.86241e6i	0.0531428	+	0.673809i
$449$			5.36707e6i			1.25638i	0.778059	+	0.628191i	$0.216204\pi$
$449$			5.36707e6i			1.25638i	−0.778059	+	0.628191i	$0.783796\pi$
$450$	−2.39657e7	−	1.34206e7i	−5.57903	−	3.12420i
$451$			3.64973e6i			0.844927i
$452$	3.13485e6	−	1.92128e6i	0.721723	−	0.442328i
$453$			6.60195e6i			1.51156i
$454$	1.33901e6	−	2.39113e6i	0.304890	−	0.544456i
$455$	3.94207e6			0.892680
$456$	−4.31645e6	+	6.87664e6i	−0.972108	+	1.54869i
$457$	3.00983e6			0.674142			0.337071	−	0.941479i	$-0.390564\pi$
$457$	3.00983e6			0.674142			0.337071	+	0.941479i	$0.390564\pi$
$458$	2.85009e6	−	5.08953e6i	0.634884	−	1.13374i
$459$		−	3.58082e6i		−	0.793324i
$460$	8.00650e6	+	1.30638e7i	1.76420	+	2.87855i
$461$		−	1.70263e6i		−	0.373137i	−0.982442	−	0.186568i	$-0.940263\pi$
$461$		−	1.70263e6i		−	0.373137i	0.982442	−	0.186568i	$-0.0597366\pi$
$462$	−6.00222e6	−	3.36119e6i	−1.30830	−	0.732635i
$463$		−	5.09539e6i		−	1.10465i	−0.833629	−	0.552325i	$-0.813741\pi$
$463$		−	5.09539e6i		−	1.10465i	0.833629	−	0.552325i	$-0.186259\pi$
$464$	2.14621e6	−	4.21333e6i	0.462783	−	0.908512i
$465$	−3.97030e6			−0.851513
$466$	−5.83152e6	−	3.26560e6i	−1.24399	−	0.696623i
$467$	−8.38901e6			−1.77999			−0.889997	−	0.455967i	$-0.849293\pi$
$467$	−8.38901e6			−1.77999			−0.889997	+	0.455967i	$0.849293\pi$
$468$	3.96855e6	+	6.47528e6i	0.837562	+	1.36661i
$469$	2.78024e6			0.583647
$470$	2.45972e6	+	1.37742e6i	0.513619	+	0.287622i
$471$	−414079.			−0.0860064
$472$	5.21661e6	−	205396.i	1.07779	−	0.0424363i
$473$	−1.62243e6			−0.333435
$474$	−2.63354e6	+	4.70283e6i	−0.538386	+	0.961421i
$475$	7.57485e6	−	1.10747e7i	1.54042	−	2.25216i
$476$	920007.	−	563851.i	0.186112	−	0.114064i
$477$	1.22078e7			2.45664
$478$	−404998.	+	723223.i	−0.0810742	+	0.144778i
$479$			6.30836e6i			1.25626i	0.778110	+	0.628128i	$0.216178\pi$
$479$			6.30836e6i			1.25626i	−0.778110	+	0.628128i	$0.783822\pi$
$480$	1.48176e7	−	9.90376e6i	2.93544	−	1.96199i
$481$	−2.08141e6			−0.410199
$482$	3.16594e6	−	5.65356e6i	0.620705	−	1.10842i
$483$			1.10790e7i			2.16088i
$484$	1.27116e6	+	2.07409e6i	0.246653	+	0.402452i
$485$	5.21586e6			1.00687
$486$	3.74393e6	−	6.68571e6i	0.719014	−	1.28398i
$487$	−852875.			−0.162953			−0.0814766	−	0.996675i	$-0.525964\pi$
$487$	−852875.			−0.162953			−0.0814766	+	0.996675i	$0.525964\pi$
$488$	1.89346e6	−	74552.0i	0.359920	−	0.0141713i
$489$			1.04101e7i			1.96871i
$490$	−2.72357e6	+	4.86360e6i	−0.512446	+	0.915097i
$491$	1.03276e7			1.93328			0.966639	−	0.256141i	$-0.0824512\pi$
$491$	1.03276e7			1.93328			0.966639	+	0.256141i	$0.0824512\pi$
$492$	−3.57269e6	−	5.82937e6i	−0.665400	−	1.08570i
$493$	−1.77698e6			−0.329279
$494$	−3.32353e6	+	1.64840e6i	−0.612749	+	0.303910i
$495$			2.99291e7i			5.49011i
$496$	599763.	−	1.17743e6i	0.109465	−	0.214896i
$497$			737263.i			0.133885i
$498$	−4.71058e6	+	8.41189e6i	−0.851140	+	1.51992i
$499$	−1.67531e6			−0.301192			−0.150596	−	0.988595i	$-0.548119\pi$
$499$	−1.67531e6			−0.301192			−0.150596	+	0.988595i	$0.548119\pi$
$500$	−1.59088e7	+	9.75013e6i	−2.84585	+	1.74416i
$501$			1.84456e6i			0.328321i
$502$	9.56550e6	+	5.35659e6i	1.69414	+	0.948700i
$503$		−	7.29065e6i		−	1.28483i	−0.766356	−	0.642416i	$-0.777932\pi$
$503$		−	7.29065e6i		−	1.28483i	0.766356	−	0.642416i	$-0.222068\pi$
$504$	9.02559e6	−	355369.i	1.58270	−	0.0623165i
$505$	1.15832e7			2.02115
$506$	5.96947e6	−	1.06600e7i	1.03648	−	1.85088i
$507$		−	5.63213e6i		−	0.973089i
$508$	1.34818e6	+	2.19976e6i	0.231787	+	0.378196i
$509$	−4.39175e6			−0.751352			−0.375676	−	0.926751i	$-0.622589\pi$
$509$	−4.39175e6			−0.751352			−0.375676	+	0.926751i	$0.622589\pi$
$510$	−5.84390e6	−	3.27253e6i	−0.994895	−	0.557132i
$511$		−	1.40019e6i		−	0.237212i
$512$	698661.	+	5.89035e6i	0.117785	+	0.993039i
$513$	1.20856e7	+	8.26625e6i	2.02756	+	1.38680i
$514$	3.97547e6	−	7.09918e6i	0.663714	−	1.18522i
$515$			1.13206e7i			1.88083i
$516$	2.59135e6	−	1.58818e6i	0.428452	−	0.262588i
$517$		−	2.24793e6i		−	0.369876i
$518$	−1.20952e6	+	2.15989e6i	−0.198056	+	0.353678i
$519$			6.85267e6i			1.11671i
$520$	8.13737e6	−	320397.i	1.31970	−	0.0519613i
$521$		−	5.36102e6i		−	0.865272i	−0.901569	−	0.432636i	$-0.857583\pi$
$521$		−	5.36102e6i		−	0.865272i	0.901569	−	0.432636i	$-0.142417\pi$
$522$	−1.29785e7	−	7.26782e6i	−2.08472	−	1.16742i
$523$			2.33893e6i			0.373906i	0.982369	+	0.186953i	$0.0598612\pi$
$523$			2.33893e6i			0.373906i	−0.982369	+	0.186953i	$0.940139\pi$
$524$	397626.	+	648785.i	0.0632625	+	0.103222i
$525$	−2.12968e7			−3.37222
$526$	2.58575e6	−	4.61749e6i	0.407495	−	0.727682i
$527$	−496580.			−0.0778867
$528$	−1.26632e7	−	6.45045e6i	−1.97678	−	1.00694i
$529$	−1.32399e7			−2.05706
$530$	6.39590e6	−	1.14214e7i	0.989036	−	1.76617i
$531$		−	1.64232e7i		−	2.52768i
$532$	−220768.	+	4.40675e6i	−0.0338187	+	0.675055i
$533$		−	3.12407e6i		−	0.476324i
$534$	−1.33722e7	−	7.48829e6i	−2.02931	−	1.13640i
$535$	2.15103e7			3.24909
$536$	5.73908e6	−	225968.i	0.862841	−	0.0339730i
$537$	−7.82950e6			−1.17165
$538$	8.46840e6	+	4.74222e6i	1.26138	+	0.706360i
$539$	4.44482e6			0.658996
$540$	−1.67955e7	−	2.74043e7i	−2.47861	−	4.04421i
$541$			7.80271e6i			1.14618i	0.819493	+	0.573089i	$0.194255\pi$
$541$			7.80271e6i			1.14618i	−0.819493	+	0.573089i	$0.805745\pi$
$542$	−3.07696e6	+	5.49467e6i	−0.449909	+	0.803422i
$543$		−	1.57681e7i		−	2.29499i
$544$	1.85329e6	−	1.23870e6i	0.268501	−	0.179460i
$545$			1.37067e7i			1.97670i
$546$	5.13774e6	+	2.87708e6i	0.737548	+	0.413020i
$547$			2.08885e6i			0.298496i	0.988800	+	0.149248i	$0.0476853\pi$
$547$			2.08885e6i			0.298496i	−0.988800	+	0.149248i	$0.952315\pi$
$548$	742280.	+	1.21114e6i	0.105588	+	0.172283i
$549$		−	5.96108e6i		−	0.844100i
$550$	2.04913e7	+	1.14750e7i	2.88844	+	1.61750i
$551$	4.10211e6	−	5.99746e6i	0.575611	−	0.841566i
$552$	900457.	+	2.28696e7i	0.125781	+	3.19456i
$553$			2.92916e6i			0.407315i
$554$	1.59278e6	−	2.84429e6i	0.220486	−	0.393731i
$555$	1.53658e7			2.11749
$556$	−4.43684e6	−	7.23937e6i	−0.608677	−	0.993147i
$557$			2.39511e6i			0.327105i	0.986535	+	0.163552i	$0.0522953\pi$
$557$			2.39511e6i			0.327105i	−0.986535	+	0.163552i	$0.947705\pi$
$558$	−3.62686e6	−	2.03101e6i	−0.493112	−	0.276138i
$559$	1.38875e6			0.187973
$560$	4.39620e6	−	8.63039e6i	0.592389	−	1.16295i
$561$			5.34072e6i			0.716461i
$562$	−3.22655e6	+	5.76180e6i	−0.430922	+	0.769516i
$563$		−	3.08044e6i		−	0.409583i	−0.978806	−	0.204792i	$-0.934348\pi$
$563$		−	3.08044e6i		−	0.409583i	0.978806	−	0.204792i	$-0.0656517\pi$
$564$	2.20048e6	+	3.59041e6i	0.291286	+	0.475276i
$565$	−1.24026e7			−1.63452
$566$	−7.15431e6	−	4.00635e6i	−0.938700	−	0.525663i
$567$		−	1.11153e7i		−	1.45200i
$568$	59922.0	+	1.52189e6i	0.00779319	+	0.197930i
$569$			1.47624e6i			0.191151i	0.995422	+	0.0955756i	$0.0304692\pi$
$569$			1.47624e6i			0.191151i	−0.995422	+	0.0955756i	$0.969531\pi$
$570$	2.45356e7	−	1.21691e7i	3.16308	−	1.56882i
$571$	−3.25915e6			−0.418326			−0.209163	−	0.977881i	$-0.567074\pi$
$571$	−3.25915e6			−0.418326			−0.209163	+	0.977881i	$0.567074\pi$
$572$	−3.39322e6	−	5.53655e6i	−0.433633	−	0.707537i
$573$	1.61552e7			2.05553
$574$	−3.24187e6	−	1.81542e6i	−0.410691	−	0.229983i
$575$		−	3.78232e7i		−	4.77077i
$576$	1.86021e7	−	1.46713e6i	2.33618	−	0.184252i
$577$	5.09234e6			0.636763			0.318382	−	0.947963i	$-0.396861\pi$
$577$	5.09234e6			0.636763			0.318382	+	0.947963i	$0.396861\pi$
$578$	6.27701e6	+	3.51507e6i	0.781508	+	0.437637i
$579$	1.94458e7			2.41062
$580$	−1.35993e7	+	8.33472e6i	−1.67860	+	1.02878i
$581$			5.23936e6i			0.643928i
$582$	6.79788e6	+	3.80675e6i	0.831890	+	0.465851i
$583$	−1.04380e7			−1.27188
$584$	−113803.	−	2.89034e6i	−0.0138077	−	0.350684i
$585$		−	2.56185e7i		−	3.09503i
$586$	−2.21223e6	−	1.23883e6i	−0.266125	−	0.149028i
$587$	−5.57945e6			−0.668338			−0.334169	−	0.942513i	$-0.608456\pi$
$587$	−5.57945e6			−0.668338			−0.334169	+	0.942513i	$0.608456\pi$
$588$	−7.09931e6	+	4.35100e6i	−0.846784	+	0.518975i
$589$	1.14635e6	−	1.67600e6i	0.136153	−	0.199061i
$590$	−1.53653e7	−	8.60444e6i	−1.81724	−	1.01764i
$591$	5.76345e6			0.678756
$592$	−2.32119e6	+	4.55684e6i	−0.272211	+	0.534392i
$593$	9.80184e6			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$593$	9.80184e6			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$594$	−1.25223e7	+	2.23617e7i	−1.45619	+	2.60039i
$595$	−3.63988e6			−0.421497
$596$	5.17110e6	−	3.16925e6i	0.596304	−	0.365461i
$597$	−1.61196e6			−0.185106
$598$	−5.10971e6	+	9.12464e6i	−0.584310	+	1.04343i
$599$	1.68384e7			1.91749			0.958746	−	0.284263i	$-0.0917489\pi$
$599$	1.68384e7			1.91749			0.958746	+	0.284263i	$0.0917489\pi$
$600$	−4.39617e7	+	1.73092e6i	−4.98536	+	0.196291i
$601$		−	6.92827e6i		−	0.782417i	−0.920302	−	0.391209i	$-0.872057\pi$
$601$		−	6.92827e6i		−	0.782417i	0.920302	−	0.391209i	$-0.127943\pi$
$602$	807012.	−	1.44112e6i	0.0907588	−	0.162072i
$603$		−	1.80681e7i		−	2.02357i
$604$	3.87300e6	+	6.31937e6i	0.431971	+	0.704825i
$605$		−	8.20583e6i		−	0.911453i
$606$	1.50965e7	+	8.45387e6i	1.66991	+	0.935135i
$607$	−9.90735e6			−1.09140			−0.545702	−	0.837979i	$-0.683737\pi$
$607$	−9.90735e6			−1.09140			−0.545702	+	0.837979i	$0.683737\pi$
$608$	−97553.3	+	9.11453e6i	−0.0107024	+	0.999943i
$609$	−1.15331e7			−1.26010
$610$	−5.57710e6	−	3.12312e6i	−0.606854	−	0.339832i
$611$			1.92417e6i			0.208516i
$612$	−3.66433e6	−	5.97890e6i	−0.395472	−	0.645271i
$613$			9.14242e6i			0.982676i	0.870969	+	0.491338i	$0.163492\pi$
$613$			9.14242e6i			0.982676i	−0.870969	+	0.491338i	$0.836508\pi$
$614$	−7.22961e6	+	1.29102e7i	−0.773916	+	1.38202i
$615$			2.30631e7i			2.45884i
$616$	−7.71713e6	+	303850.i	−0.819416	+	0.0322632i
$617$	−4.19657e6			−0.443795			−0.221897	−	0.975070i	$-0.571225\pi$
$617$	−4.19657e6			−0.443795			−0.221897	+	0.975070i	$0.571225\pi$
$618$	−8.26222e6	+	1.47542e7i	−0.870213	+	1.55398i
$619$	−2.05006e6			−0.215050			−0.107525	−	0.994202i	$-0.534293\pi$
$619$	−2.05006e6			−0.215050			−0.107525	+	0.994202i	$0.534293\pi$
$620$	−3.80037e6	+	2.32916e6i	−0.397051	+	0.243343i
$621$	4.12755e7			4.29500
$622$	7.91720e6	−	1.41381e7i	0.820533	−	1.46526i
$623$	−8.32887e6			−0.859737
$624$	1.08394e7	+	5.52142e6i	1.11440	+	0.567661i
$625$	3.62946e7			3.71656
$626$	−9.59672e6	−	5.37407e6i	−0.978784	−	0.548110i
$627$	−1.80254e7	−	1.23289e7i	−1.83112	−	1.25244i
$628$	−396356.	+	242917.i	−0.0401038	+	0.0245787i
$629$	1.92185e6			0.193684
$630$	−2.65845e7	−	1.48871e7i	−2.66856	−	1.49437i
$631$		−	1.07445e6i		−	0.107427i	−0.998556	−	0.0537134i	$-0.982894\pi$
$631$		−	1.07445e6i		−	0.107427i	0.998556	−	0.0537134i	$-0.0171058\pi$
$632$	238071.	+	6.04649e6i	0.0237091	+	0.602158i
$633$	−6.22840e6			−0.617827
$634$	−484594.	−	271368.i	−0.0478801	−	0.0268124i
$635$		−	8.70305e6i		−	0.856519i
$636$	1.66717e7	−	1.02177e7i	1.63432	−	1.00164i
$637$	−3.80465e6			−0.371506
$638$	1.10970e7	+	6.21419e6i	1.07933	+	0.604412i
$639$	4.79129e6			0.464194
$640$	8.37336e6	−	1.81725e7i	0.808072	−	1.75374i
$641$			1.12011e7i			1.07675i	0.842705	+	0.538376i	$0.180962\pi$
$641$			1.12011e7i			1.07675i	−0.842705	+	0.538376i	$0.819038\pi$
$642$	2.80346e7	+	1.56991e7i	2.68446	+	1.50327i
$643$	1.00653e6			0.0960061			0.0480030	−	0.998847i	$-0.484714\pi$
$643$	1.00653e6			0.0960061			0.0480030	+	0.998847i	$0.484714\pi$
$644$	6.49942e6	+	1.06048e7i	0.617532	+	1.00760i
$645$	−1.02523e7			−0.970336
$646$	3.06876e6	−	1.52204e6i	0.289322	−	0.143497i
$647$		−	1.43017e7i		−	1.34316i	−0.740931	−	0.671581i	$-0.765616\pi$
$647$		−	1.43017e7i		−	1.34316i	0.740931	−	0.671581i	$-0.234384\pi$
$648$	−903414.	−	2.29447e7i	−0.0845180	−	2.14657i
$649$			1.40423e7i			1.30866i
$650$	−1.75400e7	−	9.82226e6i	−1.62835	−	0.911859i
$651$	−3.22297e6			−0.298060
$652$	6.10703e6	+	9.96453e6i	0.562615	+	0.917989i
$653$		−	1.06249e7i		−	0.975083i	−0.873100	−	0.487541i	$-0.837894\pi$
$653$		−	1.06249e7i		−	0.975083i	0.873100	−	0.487541i	$-0.162106\pi$
$654$	−1.00037e7	+	1.78641e7i	−0.914569	+	1.63319i
$655$		−	2.56683e6i		−	0.233772i
$656$	−6.83954e6	−	3.48396e6i	−0.620537	−	0.316092i
$657$	−9.09951e6			−0.822441
$658$	1.99672e6	+	1.11814e6i	0.179785	+	0.100678i
$659$		−	435445.i		−	0.0390589i	−0.999809	−	0.0195295i	$-0.993783\pi$
$659$		−	435445.i		−	0.0390589i	0.999809	−	0.0195295i	$-0.00621681\pi$
$660$	2.50501e7	+	4.08729e7i	2.23846	+	3.65238i
$661$	−2.13248e7			−1.89837			−0.949186	−	0.314715i	$-0.898091\pi$
$661$	−2.13248e7			−1.89837			−0.949186	+	0.314715i	$0.898091\pi$
$662$	−7.50832e6	+	1.34079e7i	−0.665883	+	1.18910i
$663$		−	4.57151e6i		−	0.403902i
$664$	425835.	+	1.08153e7i	0.0374819	+	0.951958i
$665$	8.40259e6	−	1.22849e7i	0.736816	−	1.07725i
$666$	1.40366e7	+	7.86036e6i	1.22624	+	0.686684i
$667$		−	2.04829e7i		−	1.78269i
$668$	1.08210e6	+	1.76561e6i	0.0938268	+	0.153092i
$669$		−	1.83999e7i		−	1.58947i
$670$	−1.69042e7	−	9.46622e6i	−1.45482	−	0.814685i
$671$			5.09689e6i			0.437018i
$672$	1.20284e7	−	8.03955e6i	1.02751	−	0.686766i
$673$			1.39908e7i			1.19071i	0.803464	+	0.595353i	$0.202988\pi$
$673$			1.39908e7i			1.19071i	−0.803464	+	0.595353i	$0.797012\pi$
$674$	−4.92796e6	+	8.80008e6i	−0.417847	+	0.746169i
$675$			7.93427e7i			6.70267i
$676$	−3.30406e6	−	5.39106e6i	−0.278087	−	0.453740i
$677$	−1.68979e7			−1.41697			−0.708485	−	0.705726i	$-0.750621\pi$
$677$	−1.68979e7			−1.41697			−0.708485	+	0.705726i	$0.750621\pi$
$678$	−1.61644e7	−	9.05192e6i	−1.35047	−	0.756252i
$679$	4.23406e6			0.352438
$680$	−7.51358e6	+	295836.i	−0.623124	+	0.0245346i
$681$	−1.38088e7			−1.14101
$682$	3.10107e6	+	1.73657e6i	0.255300	+	0.142966i
$683$		−	5.55844e6i		−	0.455933i	−0.973669	−	0.227967i	$-0.926792\pi$
$683$		−	5.55844e6i		−	0.455933i	0.973669	−	0.227967i	$-0.0732077\pi$
$684$	2.86383e7	+	1.43471e6i	2.34050	+	0.117253i
$685$		−	4.79171e6i		−	0.390179i
$686$	−6.28137e6	+	1.12169e7i	−0.509618	+	0.910047i
$687$	−2.93922e7			−2.37596
$688$	1.54874e6	−	3.04040e6i	0.124740	−	0.244884i
$689$	8.93466e6			0.717018
$690$	3.77219e7	−	6.73616e7i	3.01627	−	5.38629i
$691$	1.02770e6			0.0818789			0.0409394	−	0.999162i	$-0.486965\pi$
$691$	1.02770e6			0.0818789			0.0409394	+	0.999162i	$0.486965\pi$
$692$	4.02008e6	+	6.55936e6i	0.319132	+	0.520711i
$693$			2.42955e7i			1.92173i
$694$	680975.	+	381340.i	0.0536701	+	0.0300548i
$695$			2.86415e7i			2.24923i
$696$	−2.38072e7	+	937372.i	−1.86288	+	0.0733481i
$697$			2.88459e6i			0.224906i
$698$	−8.68097e6	+	1.55020e7i	−0.674419	+	1.20434i
$699$			3.36772e7i			2.60701i
$700$	−2.03852e7	+	1.24937e7i	−1.57243	+	0.963705i
$701$			1.36429e7i			1.04860i	0.851532	+	0.524302i	$0.175674\pi$
$701$			1.36429e7i			1.04860i	−0.851532	+	0.524302i	$0.824326\pi$
$702$	1.07188e7	−	1.91410e7i	0.820924	−	1.46596i
$703$	−4.43656e6	+	6.48643e6i	−0.338577	+	0.495014i
$704$	−1.59053e7	+	1.25444e6i	−1.20951	+	0.0953934i
$705$		−	1.42049e7i		−	1.07638i
$706$	−1.28919e7	−	7.21937e6i	−0.973435	−	0.545114i
$707$	9.40284e6			0.707474
$708$	−1.37459e7	−	2.24285e7i	−1.03060	−	1.68158i
$709$			1.76666e6i			0.131989i	0.997820	+	0.0659946i	$0.0210220\pi$
$709$			1.76666e6i			0.131989i	−0.997820	+	0.0659946i	$0.978978\pi$
$710$	2.51025e6	−	4.48266e6i	0.186883	−	0.333726i
$711$	1.90359e7			1.41221
$712$	−1.71928e7	+	676940.i	−1.27100	+	0.0500438i
$713$		−	5.72400e6i		−	0.421673i
$714$	−4.74389e6	−	2.65653e6i	−0.348248	−	0.195016i
$715$			2.19046e7i			1.60239i
$716$	−7.49438e6	+	4.59313e6i	−0.546327	+	0.334832i
$717$	4.17663e6			0.303409
$718$	3.77599e6	−	6.74296e6i	0.273351	−	0.488134i
$719$		−	1.18432e7i		−	0.854373i	−0.904164	−	0.427186i	$-0.859505\pi$
$719$		−	1.18432e7i		−	0.854373i	0.904164	−	0.427186i	$-0.140495\pi$
$720$	−5.60868e7	−	2.85698e7i	−4.03208	−	2.05388i
$721$			9.18967e6i			0.658358i
$722$	−1.94715e6	+	1.38709e7i	−0.139013	+	0.990291i
$723$	−3.26495e7			−2.32290
$724$	−9.25027e6	−	1.50932e7i	−0.655856	−	1.07013i
$725$	3.93737e7			2.78203
$726$	5.98896e6	−	1.06947e7i	0.421706	−	0.753059i
$727$			2.23911e7i			1.57123i	0.618718	+	0.785613i	$0.287652\pi$
$727$			2.23911e7i			1.57123i	−0.618718	+	0.785613i	$0.712348\pi$
$728$	6.60566e6	−	260088.i	0.461942	−	0.0181883i
$729$	−7.78534e6			−0.542574
$730$	−4.76741e6	+	8.51338e6i	−0.331112	+	0.591282i
$731$	−1.28229e6			−0.0887552
$732$	−4.98931e6	−	8.14080e6i	−0.344162	−	0.561551i
$733$		−	2.15794e7i		−	1.48347i	−0.670690	−	0.741737i	$-0.734002\pi$
$733$		−	2.15794e7i		−	1.48347i	0.670690	−	0.741737i	$-0.265998\pi$
$734$	−3.84646e6	+	6.86879e6i	−0.263524	+	0.470587i
$735$	2.80874e7			1.91776
$736$	1.42783e7	+	2.13625e7i	0.971585	+	1.45364i
$737$			1.54487e7i			1.04767i
$738$	−1.17979e7	+	2.10681e7i	−0.797379	+	1.42392i
$739$	9.51318e6			0.640788			0.320394	−	0.947284i	$-0.396185\pi$
$739$	9.51318e6			0.640788			0.320394	+	0.947284i	$0.396185\pi$
$740$	1.47081e7	−	9.01425e6i	0.987363	−	0.605132i
$741$	1.54293e7	+	1.05532e7i	1.03229	+	0.706058i
$742$	5.19199e6	−	9.27156e6i	0.346197	−	0.618220i
$743$	4.02857e6			0.267719			0.133859	−	0.991000i	$-0.457263\pi$
$743$	4.02857e6			0.267719			0.133859	+	0.991000i	$0.457263\pi$
$744$	−6.65297e6	+	261951.i	−0.440639	+	0.0173495i
$745$	−2.04587e7			−1.35048
$746$	7.16454e6	+	4.01208e6i	0.471348	+	0.263950i
$747$	3.40493e7			2.23258
$748$	3.13311e6	+	5.11213e6i	0.204749	+	0.334078i
$749$	1.74614e7			1.13730
$750$	8.20314e7	+	4.59368e7i	5.32509	+	2.98200i
$751$	−1.54309e7			−0.998370			−0.499185	−	0.866495i	$-0.666367\pi$
$751$	−1.54309e7			−0.998370			−0.499185	+	0.866495i	$0.666367\pi$
$752$	4.21259e6	+	2.14583e6i	0.271647	+	0.138373i
$753$		−	5.52410e7i		−	3.55037i
$754$	−9.49870e6	−	5.31918e6i	−0.608465	−	0.340735i
$755$		−	2.50017e7i		−	1.59625i
$756$	−1.36340e7	−	2.22459e7i	−0.867599	−	1.41562i
$757$			5.44099e6i			0.345095i	0.985001	+	0.172547i	$0.0551998\pi$
$757$			5.44099e6i			0.345095i	−0.985001	+	0.172547i	$0.944800\pi$
$758$	−1.24167e7	+	2.21731e7i	−0.784936	+	1.40170i
$759$	−6.15616e7			−3.87887
$760$	1.63465e7	−	2.60420e7i	1.02657	−	1.63546i
$761$	3.57369e6			0.223694			0.111847	−	0.993725i	$-0.464323\pi$
$761$	3.57369e6			0.223694			0.111847	+	0.993725i	$0.464323\pi$
$762$	6.35184e6	−	1.13428e7i	0.396289	−	0.707671i
$763$			1.11266e7i			0.691915i
$764$	1.54637e7	−	9.47734e6i	0.958473	−	0.587426i
$765$			2.36547e7i			1.46138i
$766$	−1.90307e7	−	1.06570e7i	−1.17188	−	0.656241i
$767$		−	1.20199e7i		−	0.737753i
$768$	2.41761e7	−	1.75732e7i	1.47905	−	1.07510i
$769$	1.22202e7			0.745184			0.372592	−	0.927995i	$-0.378469\pi$
$769$	1.22202e7			0.745184			0.372592	+	0.927995i	$0.378469\pi$
$770$	2.27305e7	+	1.27289e7i	1.38160	+	0.773683i
$771$	−4.09980e7			−2.48386
$772$	1.86135e7	−	1.14078e7i	1.12405	−	0.688902i
$773$	1.90679e7			1.14777			0.573885	−	0.818936i	$-0.305436\pi$
$773$	1.90679e7			1.14777			0.573885	+	0.818936i	$0.305436\pi$
$774$	−9.36546e6	−	5.24457e6i	−0.561923	−	0.314672i
$775$	1.10031e7			0.658052
$776$	8.74012e6	−	344129.i	0.521031	−	0.0205148i
$777$	1.24734e7			0.741197
$778$	1.52691e7	−	2.72666e7i	0.904405	−	1.61504i
$779$	−9.73574e6	−	6.65901e6i	−0.574811	−	0.393157i
$780$	−2.14422e7	−	3.49861e7i	−1.26192	−	2.05901i
$781$	−4.09669e6			−0.240328
$782$	4.71801e6	−	8.42516e6i	0.275894	−	0.492676i
$783$			4.29676e7i			2.50459i
$784$	−4.24295e6	+	8.32954e6i	−0.246534	+	0.483984i
$785$	1.56812e6			0.0908252
$786$	1.87338e6	−	3.34537e6i	0.108160	−	0.193147i
$787$		−	3.45195e6i		−	0.198668i	−0.995054	−	0.0993339i	$-0.968329\pi$
$787$		−	3.45195e6i		−	0.198668i	0.995054	−	0.0993339i	$-0.0316712\pi$
$788$	5.51676e6	−	3.38110e6i	0.316496	−	0.193973i
$789$	−2.66661e7			−1.52499
$790$	9.97326e6	−	1.78097e7i	0.568551	−	1.01529i
$791$	−1.00680e7			−0.572141
$792$	1.97465e6	+	5.01517e7i	0.111860	+	2.84101i
$793$		−	4.36280e6i		−	0.246367i
$794$	6.85331e6	−	1.22383e7i	0.385789	−	0.688920i
$795$	−6.59592e7			−3.70133
$796$	−1.54297e6	+	945650.i	−0.0863127	+	0.0528991i
$797$	1.76442e6			0.0983909			0.0491955	−	0.998789i	$-0.484334\pi$
$797$	1.76442e6			0.0983909			0.0491955	+	0.998789i	$0.484334\pi$
$798$	1.99172e7	−	9.87851e6i	1.10719	−	0.549142i
$799$		−	1.77666e6i		−	0.0984551i
$800$	−4.10646e7	+	2.74467e7i	−2.26852	+	1.51623i
$801$			5.41272e7i			2.98081i
$802$	−7.17345e6	+	1.28099e7i	−0.393815	+	0.703253i
$803$	7.78034e6			0.425804
$804$	−1.51226e7	−	2.46748e7i	−0.825064	−	1.34621i
$805$		−	4.19562e7i		−	2.28195i
$806$	−2.65444e6	−	1.48646e6i	−0.143924	−	0.0805963i
$807$		−	4.89052e7i		−	2.64345i
$808$	1.94097e7	−	764228.i	1.04590	−	0.0411808i
$809$	−2.93512e7			−1.57672			−0.788360	−	0.615214i	$-0.789069\pi$
$809$	−2.93512e7			−1.57672			−0.788360	+	0.615214i	$0.789069\pi$
$810$	−3.78457e7	+	6.75828e7i	−2.02677	+	3.61929i
$811$		−	657773.i		−	0.0351175i	−0.999846	−	0.0175588i	$-0.994411\pi$
$811$		−	657773.i		−	0.0351175i	0.999846	−	0.0175588i	$-0.00558942\pi$
$812$	−1.10395e7	+	6.76586e6i	−0.587570	+	0.360108i
$813$	3.17319e7			1.68372
$814$	−1.20017e7	−	6.72083e6i	−0.634865	−	0.355518i
$815$		−	3.94232e7i		−	2.07902i
$816$	−1.00084e7	−	5.09816e6i	−0.526188	−	0.268033i
$817$	2.96015e6	−	4.32786e6i	0.155152	−	0.226839i
$818$	−8.42906e6	+	1.50522e7i	−0.440449	+	0.786530i
$819$		−	2.07963e7i		−	1.08337i
$820$	1.35298e7	+	2.20759e7i	0.702681	+	1.14653i
$821$			2.24178e7i			1.16074i	0.814352	+	0.580371i	$0.197093\pi$
$821$			2.24178e7i			1.16074i	−0.814352	+	0.580371i	$0.802907\pi$
$822$	3.49718e6	−	6.24508e6i	0.180526	−	0.322373i
$823$			2.34801e7i			1.20837i	0.796843	+	0.604187i	$0.206502\pi$
$823$			2.34801e7i			1.20837i	−0.796843	+	0.604187i	$0.793498\pi$
$824$	746903.	+	1.89697e7i	0.0383218	+	0.973290i
$825$		−	1.18338e8i		−	6.05327i
$826$	−1.24731e7	−	6.98481e6i	−0.636098	−	0.356209i
$827$		−	1.52128e7i		−	0.773475i	−0.922190	−	0.386738i	$-0.873602\pi$
$827$		−	1.52128e7i		−	0.773475i	0.922190	−	0.386738i	$-0.126398\pi$
$828$	6.89177e7	−	4.22381e7i	3.49345	−	2.14106i
$829$	8.99072e6			0.454368			0.227184	−	0.973852i	$-0.427048\pi$
$829$	8.99072e6			0.454368			0.227184	+	0.973852i	$0.427048\pi$
$830$	1.78391e7	−	3.18560e7i	0.898828	−	1.60508i
$831$	−1.64259e7			−0.825136
$832$	1.36145e7	−	1.07377e6i	0.681858	−	0.0537776i
$833$	3.51299e6			0.175414
$834$	−2.09038e7	+	3.73288e7i	−1.04066	+	1.85836i
$835$		−	6.98538e6i		−	0.346716i
$836$	−2.44866e7	−	1.22672e6i	−1.21175	−	0.0607058i
$837$			1.20074e7i			0.592427i
$838$	8.26534e6	+	4.62851e6i	0.406584	+	0.227683i
$839$	−2.86242e7			−1.40387			−0.701937	−	0.712239i	$-0.747681\pi$
$839$	−2.86242e7			−1.40387			−0.701937	+	0.712239i	$0.747681\pi$
$840$	−4.87655e7	+	1.92007e6i	−2.38460	+	0.0938899i
$841$	811449.			0.0395613
$842$	3.20250e6	+	1.79337e6i	0.155671	+	0.0871745i
$843$	3.32746e7			1.61266
$844$	−5.96181e6	+	3.65386e6i	−0.288086	+	0.176561i
$845$			2.13290e7i			1.02761i
$846$	7.26654e6	−	1.29762e7i	0.349061	−	0.623335i
$847$		−	6.66123e6i		−	0.319041i
$848$	9.96394e6	−	1.95607e7i	0.475819	−	0.934103i
$849$			4.13163e7i			1.96722i
$850$	1.61955e7	+	9.06930e6i	0.768858	+	0.430553i
$851$			2.21529e7i			1.04859i
$852$	6.54326e6	−	4.01021e6i	0.308813	−	0.189264i
$853$			2.64820e6i			0.124617i	0.998057	+	0.0623087i	$0.0198463\pi$
$853$			2.64820e6i			0.124617i	−0.998057	+	0.0623087i	$0.980154\pi$
$854$	−4.52731e6	−	2.53525e6i	−0.212420	−	0.118953i
$855$	−7.98366e7	−	5.46063e7i	−3.73497	−	2.55463i
$856$	3.60444e7	−	1.41919e6i	1.68133	−	0.0661999i
$857$			1.75279e7i			0.815227i	0.913154	+	0.407614i	$0.133639\pi$
$857$			1.75279e7i			0.815227i	−0.913154	+	0.407614i	$0.866361\pi$
$858$	−1.59869e7	+	2.85484e7i	−0.741387	+	1.32393i
$859$	−1.40420e7			−0.649300			−0.324650	−	0.945834i	$-0.605247\pi$
$859$	−1.40420e7			−0.649300			−0.324650	+	0.945834i	$0.605247\pi$
$860$	−9.81349e6	+	6.01446e6i	−0.452457	+	0.277301i
$861$			1.87219e7i			0.860680i
$862$	3.79909e6	+	2.12745e6i	0.174145	+	0.0975196i
$863$	−1.99615e6			−0.0912358			−0.0456179	−	0.998959i	$-0.514526\pi$
$863$	−1.99615e6			−0.0912358			−0.0456179	+	0.998959i	$0.514526\pi$
$864$	−2.99519e7	−	4.48128e7i	−1.36502	−	2.04229i
$865$		−	2.59512e7i		−	1.17928i
$866$	−8.35088e6	+	1.49125e7i	−0.378388	+	0.675704i
$867$		−	3.62499e7i		−	1.63779i
$868$	−3.08502e6	+	1.89074e6i	−0.138982	+	0.0851788i
$869$	−1.62762e7			−0.731146
$870$	7.01231e7	+	3.92683e7i	3.14096	+	1.75891i
$871$		−	1.32237e7i		−	0.590619i
$872$	904333.	+	2.29681e7i	0.0402751	+	1.02290i
$873$		−	2.75161e7i		−	1.22195i
$874$	1.75443e7	+	3.53730e7i	0.776885	+	1.56637i
$875$	5.10933e7			2.25603
$876$	−1.24268e7	+	7.61612e6i	−0.547142	+	0.335331i
$877$	−3.73211e7			−1.63854			−0.819268	−	0.573411i	$-0.805620\pi$
$877$	−3.73211e7			−1.63854			−0.819268	+	0.573411i	$0.805620\pi$
$878$	−6.40287e6	−	3.58555e6i	−0.280310	−	0.156971i
$879$			1.27757e7i			0.557715i
$880$	4.79558e7	+	2.44280e7i	2.08754	+	1.06336i
$881$	−3.37709e6			−0.146589			−0.0732947	−	0.997310i	$-0.523351\pi$
$881$	−3.37709e6			−0.146589			−0.0732947	+	0.997310i	$0.523351\pi$
$882$	2.56578e7	+	1.43681e7i	1.11057	+	0.621911i
$883$	−3.62547e6			−0.156481			−0.0782407	−	0.996934i	$-0.524930\pi$
$883$	−3.62547e6			−0.156481			−0.0782407	+	0.996934i	$0.524930\pi$
$884$	−2.68185e6	−	4.37584e6i	−0.115426	−	0.188335i
$885$			8.87352e7i			3.80836i
$886$	−6.01879e6	−	3.37046e6i	−0.257587	−	0.144246i
$887$	3.24080e7			1.38307			0.691533	−	0.722345i	$-0.256936\pi$
$887$	3.24080e7			1.38307			0.691533	+	0.722345i	$0.256936\pi$
$888$	2.57482e7	−	1.01380e6i	1.09576	−	0.0431437i
$889$		−	7.06485e6i		−	0.299812i
$890$	5.06406e7	+	2.83583e7i	2.14301	+	1.20007i
$891$	6.17637e7			2.60639
$892$	−1.07942e7	−	1.76124e7i	−0.454234	−	0.741150i
$893$	5.99640e6	+	4.10139e6i	0.251630	+	0.172109i
$894$	−2.66641e7	−	1.49316e7i	−1.11579	−	0.624832i
$895$	2.96504e7			1.23730
$896$	6.79722e6	−	1.47519e7i	0.282854	−	0.613870i
$897$	5.26950e7			2.18670
$898$	1.48342e7	−	2.64900e7i	0.613864	−	1.09621i
$899$	5.95865e6			0.245894
$900$	8.11931e7	+	1.32479e8i	3.34128	+	5.45179i
$901$	−8.24975e6			−0.338555
$902$	1.00876e7	−	1.80138e7i	0.412829	−	0.737207i
$903$	−8.32249e6			−0.339652
$904$	−2.07828e7	+	818292.i	−0.845830	+	0.0333033i
$905$			5.97141e7i			2.42357i
$906$	1.82473e7	−	3.25850e7i	0.738546	−	1.31885i
$907$		−	9.21912e6i		−	0.372110i	−0.982539	−	0.186055i	$-0.940430\pi$
$907$		−	9.21912e6i		−	0.372110i	0.982539	−	0.186055i	$-0.0595703\pi$
$908$	−1.32178e7	+	8.10087e6i	−0.532039	+	0.326075i
$909$		−	6.11067e7i		−	2.45290i
$910$	−1.94567e7	−	1.08956e7i	−0.778872	−	0.436161i
$911$	2.58114e7			1.03042			0.515212	−	0.857063i	$-0.327713\pi$
$911$	2.58114e7			1.03042			0.515212	+	0.857063i	$0.327713\pi$
$912$	4.03110e7	−	2.20104e7i	1.60486	−	0.876276i
$913$	−2.91131e7			−1.15588
$914$	−1.48555e7	−	8.31893e6i	−0.588195	−	0.329384i
$915$			3.22079e7i			1.27177i
$916$	−2.81341e7	+	1.72428e7i	−1.10789	+	0.678998i
$917$		−	2.08367e6i		−	0.0818286i
$918$	−9.89710e6	+	1.76737e7i	−0.387616	+	0.692183i
$919$			4.04625e7i			1.58039i	0.612856	+	0.790194i	$0.290020\pi$
$919$			4.04625e7i			1.58039i	−0.612856	+	0.790194i	$0.709980\pi$
$920$	−3.41005e6	−	8.66077e7i	−0.132828	−	3.37355i
$921$	7.45569e7			2.89627
$922$	−4.70594e6	+	8.40360e6i	−0.182314	+	0.325565i
$923$	3.50665e6			0.135484
$924$	2.03349e7	+	3.31793e7i	0.783540	+	1.27846i
$925$	−4.25839e7			−1.63640
$926$	−1.40832e7	+	2.51491e7i	−0.539729	+	0.963817i
$927$	5.97214e7			2.28260
$928$	−2.22383e7	+	1.48636e7i	−0.847679	+	0.566571i
$929$	−191349.			−0.00727424			−0.00363712	−	0.999993i	$-0.501158\pi$
$929$	−191349.			−0.00727424			−0.00363712	+	0.999993i	$0.501158\pi$
$930$	1.95961e7	+	1.09736e7i	0.742953	+	0.416047i
$931$	−8.10967e6	+	1.18567e7i	−0.306640	+	0.448321i
$932$	1.97565e7	+	3.22357e7i	0.745026	+	1.21562i
$933$	−8.16480e7			−3.07073
$934$	4.14053e7	+	2.31866e7i	1.55306	+	0.869699i
$935$		−	2.02254e7i		−	0.756603i
$936$	−1.69025e6	−	4.29285e7i	−0.0630609	−	1.60161i
$937$	−2.88130e7			−1.07211			−0.536056	−	0.844183i	$-0.680086\pi$
$937$	−2.88130e7			−1.07211			−0.536056	+	0.844183i	$0.680086\pi$
$938$	−1.37223e7	−	7.68437e6i	−0.509238	−	0.285168i
$939$			5.54213e7i			2.05122i
$940$	−8.33325e6	−	1.35969e7i	−0.307606	−	0.501905i
$941$	5.02395e7			1.84957			0.924785	−	0.380489i	$-0.124244\pi$
$941$	5.02395e7			1.84957			0.924785	+	0.380489i	$0.124244\pi$
$942$	2.04375e6	+	1.14448e6i	0.0750414	+	0.0420225i
$943$	−3.32501e7			−1.21763
$944$	−2.63151e7	−	1.34045e7i	−0.961115	−	0.489578i
$945$			8.80128e7i			3.20602i
$946$	8.00774e6	+	4.48426e6i	0.290926	+	0.162916i
$947$	1.96661e7			0.712597			0.356298	−	0.934372i	$-0.384039\pi$
$947$	1.96661e7			0.712597			0.356298	+	0.934372i	$0.384039\pi$
$948$	2.59965e7	−	1.59327e7i	0.939495	−	0.575795i
$949$	−6.65977e6			−0.240045
$950$	−6.79966e7	+	3.37249e7i	−2.44443	+	1.21239i
$951$			2.79855e6i			0.100342i
$952$	−6.09928e6	+	240150.i	−0.218115	+	0.00858797i
$953$		−	4.08757e7i		−	1.45792i	−0.684558	−	0.728958i	$-0.740005\pi$
$953$		−	4.08757e7i		−	1.45792i	0.684558	−	0.728958i	$-0.259995\pi$
$954$	−6.02536e7	−	3.37414e7i	−2.14344	−	1.20031i
$955$	−6.11799e7			−2.17070
$956$	3.99786e6	−	2.45020e6i	0.141476	−	0.0867075i
$957$		−	6.40853e7i		−	2.26193i
$958$	1.74358e7	−	3.11359e7i	0.613802	−	1.09609i
$959$		−	3.88975e6i		−	0.136576i
$960$	−1.00508e8	+	7.92697e6i	−3.51983	+	0.277606i
$961$	−2.69640e7			−0.941837
$962$	1.02731e7	+	5.75285e6i	0.357903	+	0.200422i
$963$		−	1.13477e8i		−	3.94314i
$964$	−3.12520e7	+	1.91536e7i	−1.08314	+	0.663833i
$965$	−7.36416e7			−2.54569
$966$	3.06214e7	−	5.46820e7i	1.05580	−	1.88539i
$967$		−	3.72816e7i		−	1.28212i	−0.767492	−	0.641059i	$-0.778495\pi$
$967$		−	3.72816e7i		−	1.28212i	0.767492	−	0.641059i	$-0.221505\pi$
$968$	−541400.	−	1.37504e7i	−0.0185708	−	0.471657i
$969$	−1.42465e7	−	9.74426e6i	−0.487415	−	0.333380i
$970$	−2.57437e7	−	1.44162e7i	−0.878499	−	0.491951i
$971$		−	3.48090e7i		−	1.18479i	−0.805646	−	0.592397i	$-0.798182\pi$
$971$		−	3.48090e7i		−	1.18479i	0.805646	−	0.592397i	$-0.201818\pi$
$972$	−3.69576e7	+	2.26504e7i	−1.25469	+	0.768973i
$973$			2.32503e7i			0.787310i
$974$	4.20950e6	+	2.35728e6i	0.142178	+	0.0796185i
$975$			1.01294e8i			3.41250i
$976$	−9.55151e6	−	4.86540e6i	−0.320957	−	0.163491i
$977$			1.92230e7i			0.644296i	0.946689	+	0.322148i	$0.104405\pi$
$977$			1.92230e7i			0.644296i	−0.946689	+	0.322148i	$0.895595\pi$
$978$	2.87727e7	−	5.13807e7i	0.961908	−	1.71772i
$979$		−	4.62803e7i		−	1.54326i
$980$	2.68852e7	−	1.64773e7i	0.894228	−	0.548052i
$981$	7.23093e7			2.39895
$982$	−5.09734e7	−	2.85446e7i	−1.68680	−	0.944594i
$983$	−3.86955e7			−1.27725			−0.638626	−	0.769517i	$-0.720497\pi$
$983$	−3.86955e7			−1.27725			−0.638626	+	0.769517i	$0.720497\pi$
$984$	1.52165e6	+	3.86464e7i	0.0500986	+	1.27239i
$985$	−2.18263e7			−0.716786
$986$	8.77055e6	+	4.91143e6i	0.287299	+	0.160885i
$987$		−	1.15311e7i		−	0.376772i
$988$	2.09599e7	+	1.05004e6i	0.683119	+	0.0342227i
$989$		−	1.47808e7i		−	0.480514i
$990$	8.27217e7	−	1.47720e8i	2.68245	−	4.79017i
$991$	2.40556e7			0.778093			0.389047	−	0.921218i	$-0.372805\pi$
$991$	2.40556e7			0.778093			0.389047	+	0.921218i	$0.372805\pi$
$992$	−6.21454e6	+	4.15367e6i	−0.200507	+	0.134015i
$993$	7.74313e7			2.49197
$994$	2.03774e6	−	3.63888e6i	0.0654157	−	0.116816i
$995$	6.10454e6			0.195477
$996$	4.64996e7	−	2.84986e7i	1.48526	−	0.910279i
$997$			3.45626e6i			0.110121i	0.998483	+	0.0550604i	$0.0175351\pi$
$997$			3.45626e6i			0.110121i	−0.998483	+	0.0550604i	$0.982465\pi$
$998$	8.26875e6	+	4.63042e6i	0.262793	+	0.147162i
$999$		−	4.64707e7i		−	1.47321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.17	✓	96
4.3	odd	2		608.6.b.b.303.1		96
8.3	odd	2	inner	152.6.b.b.75.79	yes	96
8.5	even	2		608.6.b.b.303.2		96
19.18	odd	2	inner	152.6.b.b.75.80	yes	96
76.75	even	2		608.6.b.b.303.95		96
152.37	odd	2		608.6.b.b.303.96		96
152.75	even	2	inner	152.6.b.b.75.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.17	✓	96	1.1	even	1	trivial
152.6.b.b.75.18	yes	96	152.75	even	2	inner
152.6.b.b.75.79	yes	96	8.3	odd	2	inner
152.6.b.b.75.80	yes	96	19.18	odd	2	inner
608.6.b.b.303.1		96	4.3	odd	2
608.6.b.b.303.2		96	8.5	even	2
608.6.b.b.303.95		96	76.75	even	2
608.6.b.b.303.96		96	152.37	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.93566 - 2.76392i) q^{2} +28.5036i q^{3} +(16.7215 + 27.2836i) q^{4} -107.944i q^{5} +(78.7817 - 140.684i) q^{6} -87.6251i q^{7} +(-7.12184 - 180.879i) q^{8} -569.454 q^{9} +O(q^{10})\)	\(q+(-4.93566 - 2.76392i) q^{2} +28.5036i q^{3} +(16.7215 + 27.2836i) q^{4} -107.944i q^{5} +(78.7817 - 140.684i) q^{6} -87.6251i q^{7} +(-7.12184 - 180.879i) q^{8} -569.454 q^{9} +(-298.348 + 532.773i) q^{10} +486.899 q^{11} +(-777.679 + 476.622i) q^{12} -416.772 q^{13} +(-242.189 + 432.488i) q^{14} +3076.78 q^{15} +(-464.785 + 912.442i) q^{16} +384.824 q^{17} +(2810.63 + 1573.93i) q^{18} +(-888.357 + 1298.81i) q^{19} +(2945.08 - 1804.97i) q^{20} +2497.63 q^{21} +(-2403.17 - 1345.75i) q^{22} +4435.79i q^{23} +(5155.70 - 202.998i) q^{24} -8526.81 q^{25} +(2057.05 + 1151.93i) q^{26} -9305.09i q^{27} +(2390.72 - 1465.22i) q^{28} -4617.64 q^{29} +(-15185.9 - 8503.97i) q^{30} -1290.41 q^{31} +(4815.94 - 3218.87i) q^{32} +13878.4i q^{33} +(-1899.36 - 1063.62i) q^{34} -9458.56 q^{35} +(-9522.10 - 15536.7i) q^{36} +4994.11 q^{37} +(7974.45 - 3955.16i) q^{38} -11879.5i q^{39} +(-19524.7 + 768.757i) q^{40} +7495.86i q^{41} +(-12327.4 - 6903.25i) q^{42} -3332.16 q^{43} +(8141.67 + 13284.3i) q^{44} +61468.8i q^{45} +(12260.2 - 21893.6i) q^{46} -4616.83i q^{47} +(-26007.9 - 13248.0i) q^{48} +9128.84 q^{49} +(42085.4 + 23567.4i) q^{50} +10968.8i q^{51} +(-6969.05 - 11371.0i) q^{52} -21437.8 q^{53} +(-25718.5 + 45926.8i) q^{54} -52557.6i q^{55} +(-15849.6 + 624.052i) q^{56} +(-37020.9 - 25321.4i) q^{57} +(22791.1 + 12762.8i) q^{58} +28840.3i q^{59} +(51448.2 + 83945.4i) q^{60} +10468.1i q^{61} +(6369.03 + 3566.59i) q^{62} +49898.4i q^{63} +(-32666.6 + 2576.39i) q^{64} +44987.9i q^{65} +(38358.7 - 68498.9i) q^{66} +31728.8i q^{67} +(6434.82 + 10499.4i) q^{68} -126436. q^{69} +(46684.2 + 26142.7i) q^{70} -8413.83 q^{71} +(4055.56 + 103002. i) q^{72} +15979.4 q^{73} +(-24649.2 - 13803.3i) q^{74} -243044. i q^{75} +(-50290.9 - 2519.46i) q^{76} -42664.6i q^{77} +(-32834.0 + 58633.2i) q^{78} -33428.3 q^{79} +(98492.2 + 50170.5i) q^{80} +126851. q^{81} +(20718.0 - 36997.0i) q^{82} -59792.9 q^{83} +(41764.0 + 68144.2i) q^{84} -41539.2i q^{85} +(16446.4 + 9209.83i) q^{86} -131619. i q^{87} +(-3467.62 - 88069.9i) q^{88} -95051.2i q^{89} +(169895. - 303389. i) q^{90} +36519.7i q^{91} +(-121024. + 74173.0i) q^{92} -36781.3i q^{93} +(-12760.6 + 22787.1i) q^{94} +(140199. + 95892.4i) q^{95} +(91749.4 + 137271. i) q^{96} +48320.2i q^{97} +(-45056.9 - 25231.4i) q^{98} -277266. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more